Quantifying the Benefits of Targeting for Pandemic Response
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medRxiv preprint doi: https://doi.org/10.1101/2021.03.23.21254155; this version posted June 18, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license . Quantifying the Benefits of Targeting for Pandemic Response Sergio Cameloa, Dragos F. Ciocanb, Dan A. Iancub,c, Xavier S. Warnesc, and Spyros I. Zoumpoulisd aInstitute for Computational and Mathematical Engineering, Stanford University bTechnology and Operations Management, INSEAD cOperations, Information & Technology, Graduate School of Business, Stanford University dDecision Sciences, INSEAD ABSTRACT To respond to pandemics such as COVID-19, policy makers have relied on interventions that target specific age groups or activities. Such targeting is potentially contentious, so rigorously quantifying its benefits and downsides is critical for designing effective and equitable pandemic control policies. We propose a flexible modeling framework and algorithms to compute optimally targeted interventions that coordinate across two dimensions of heterogeneity: age of different groups and the specific activities that individuals engage in during the course of a day. We showcase a complete implementation in a case study focused on the COVID-19 epidemic in the Île-de-France region of France, based on hospitalization, community mobility, social contacts and economic data. We find that optimized dual-targeted policies generate substantial complementarities that lead to Pareto improvements, reducing the number of deaths and the economic losses overall and reducing the time in confinement for each age group, compared to less targeted interventions. These policies have a simple and explainable structure. Since dual-targeted policies could lead to increased discrepancies in the confinements faced by distinct groups, we also quantify the impact of requirements that explicitly limit such disparities, and find that satisfactory trade-offs may be achievable through limited targeting. Keywords: Pandemic management, Confinement, Targeted interventions, Optimization, COVID-19 Introduction The COVID-19 pandemic has forced policy makers worldwide to rely on a range of large-scale population confinement measures in an effort to contain the disease spread. In determining these measures, a key recognition has been that substantial differences exist in the health and economic impact produced by different individuals engaged in distinct activities. Targeting confinements to account for such heterogeneity could be an important lever to mitigate a pandemic’s impact, but could also lead to potentially contentious and discriminatory measures. This work is aimed at developing a rigorous framework to quantify the benefits and downsides of such targeted interventions, and applying it to the COVID-19 pandemic as a real-world case study. One real-world contentious example of targeting has been to differentiate confinements based on age groups, e.g., sheltering older individuals who might face higher health risks if infected, or restricting younger groups who might create higher infection risks. Such measures, focusing on confinements or other interventions, and targeting age or other population characteristics, have been studied in the literature (1; 2; 3; 4; 5; 6; 7; 8; 9; 10) and implemented in several settings – e.g., with stricter confinements applied to older groups in Finland (11), Ireland (12), Israel (13) and Moscow (14), or curfews applied to children and youth in Bosnia and Herzegovina (15) and Turkey (16) – but some of the measures were eventually deemed unconstitutional and overturned (13; 15). A different example of targeting has stemmed from the recognition that different activities (more specifically, population interactions in locations of certain activities), such as work, schooling, transport, leisure, result in significantly different patterns of social contacts and new infections. This has been shown to be critical when modeling pandemic spread (17; 18; 19) and has been recognized in numerous implementations that differentially confine various activities (e.g., closures of schools, workplaces, recreation venues, etc.), and even some that differentiate based on both age groups and activities (e.g., dedicated hours when only the senior population was allowed to shop at supermarkets (20)). As these examples suggest, targeted confinements have merits but also pose potentially significant downsides. On the one hand, targeting can generate improvements in both health and economic outcomes, giving policy makers an improved lever when navigating difficult trade-offs. Additionally, explicitly considering multiple dimensions of targeting simultaneously – activities and age groups – could overturn some of the prevailing insight that specific age groups should uniformly face stricter confinements. However, such granular policies are more difficult to implement, and could lead to discriminatory and potentially unfair measures. Given that some amount of targeting of activities and age groups is already in place in existing real-world NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. medRxiv preprint doi: https://doi.org/10.1101/2021.03.23.21254155; this version posted June 18, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license . policy implementations, it seems critical to quantify the relative merits of a policy that (i) targets both age-based population groups and activities, and (ii) identifies optimal interventions. We propose a rigorous modeling framework and develop a set of associated algorithms that compute optimally targeted interventions that target both age groups and activities. The framework provides quantifiable answers to the following natural research questions: How large are the health and economic benefits of dual-targeted confinements? Would dual targeting lead to significant synergies, and why? Could dual targeting reduce time in confinement for every age group? What is the relationship between the effectiveness and the level of targeting allowed across distinct groups? We showcase a proof of concept for our framework through a case study calibrated on Île-de-France data – a region of France encompassing Paris with a population of approximately 12 million. The implementation, publicly available at http://insead.arnia.ro, is flexible and portable to other geographies. Methods Our framework relies on a flexible model that captures several important real-world considerations. We extend a version of the discretized SEIR (Susceptible-Exposed-Infectious-Recovered) epidemiological model (18; 21; 22) with multiple population groups that interact with each other (SI §2). We augment the model with controls that target based on (i) age groups, and (ii) types of activities that individuals engage in. Different policy interventions can be embedded as controls: we focus on time-dependent, targeted confinements, but extend the model to mass testing in the SI; vaccinations can also be accommodated. Interventions modulate the rate of social contacts and the economic value generated, and the objective of the control problem is to minimize a combination of health and economic losses caused by deaths, illness, and activity restrictions. The model captures important resource constraints (such as hospital and ICU), and allows explicitly controlling the amount of targeting through “limited disparity” constraints that limit the difference in the extent of confinement imposed on distinct age groups. Epidemiological Model and Controls. We segment the population by age into nine groups g G ; the youngest group g 2 captures individuals with age 0-9 and the oldest those aged 80 or above. For each g, the compartmental model includes states for susceptible, exposed, infectious, quarantined infectious, recovered, and deceased individuals. We also reserve separate states for individuals who are hospitalized due to being infected, in either general hospital wards or in intensive care units (ICU). We use T to denote the time horizon of the control problem, and X t to denote the entire vector of epidemiological states at time 0 t T. Individuals interact in activities belonging to the set A = work,transport,leisure,school,home,other . These interac- { } tions generate social contacts which drive the rate of new infections. We control the SEIR dynamics by adjusting the confinement intensity in each group-activity pair over time: we let a `g(t) [0,1] denote the activity level allowed for group g and activity a at time t, expressed as a fraction of the activity level 2 a under normal course of life (no confinement). We denote `g(t)=[`g(t)]a A , ut =[`g(t)]g G and ut:t =[ut ,...,ut ]. 2 2 0 0 We propose a parametric model to map activity levels to social contacts. We use cg,h(`g,`h) to denote the mean number of total daily contacts between an individual in group g and individuals in group h across all activities when their activity levels are `g,`h, respectively. Varying the activity levels changes the social contacts according to a a a1 a a2 cg,h(`g,`h)= Â Cg,h (`g) (`h) , (1) a A · · 2 a where Cg,h denote the mean number of daily contacts in activity a under normal course (i.e., without confinement), and a a1,a2 R are parameters. We retrieve values for C from the data tool (23), which is based on the French social contact 2 g,h survey data in (24), and we estimate a1,a2 from health outcome data (25) and Google mobility data (26). When the number of patients requiring hospitalization or ICU treatment exceeds the respective capacity of available beds, we assume that patients are turned away from each age group according to a proportional rule.1 Objective. Our objective captures two criteria. The first quantifies the total deaths directly attributable to the pandemic, which we denote by Total Deaths(u0:T 1) to reflect the dependency on the specific confinement policy u0:T 1 followed.